Homework 1

github_url <- "https://github.com/BU-IE-582/fall-23-burakcetiner3/raw/main/all_ticks_wide.xlsx"
local_file_path <- "all_ticks_wide.xlsx"
download.file(url = github_url, destfile = local_file_path, mode = "wb")
Dataset <- read_excel(local_file_path)
summary(Dataset)
##   timestamp             AEFES             AKBNK             AKSA        
##  Length:50012       Min.   : 0.0001   Min.   :0.0001   Min.   : 0.0001  
##  Class :character   1st Qu.:19.1605   1st Qu.:5.8500   1st Qu.: 5.2088  
##  Mode  :character   Median :20.6465   Median :6.3057   Median : 6.9853  
##                     Mean   :20.9822   Mean   :6.4731   Mean   : 7.1275  
##                     3rd Qu.:22.7320   3rd Qu.:6.9325   3rd Qu.: 8.7200  
##                     Max.   :28.5090   Max.   :9.2124   Max.   :15.1189  
##                     NA's   :1881      NA's   :803      NA's   :1418     
##      AKSEN           ALARK            ALBRK           ANACM       
##  Min.   :0.000   Min.   :0.0001   Min.   :1.026   Min.   :0.0001  
##  1st Qu.:2.670   1st Qu.:1.5689   1st Qu.:1.225   1st Qu.:1.0470  
##  Median :2.930   Median :1.9376   Median :1.360   Median :1.2597  
##  Mean   :3.183   Mean   :2.0609   Mean   :1.365   Mean   :1.6721  
##  3rd Qu.:3.750   3rd Qu.:2.4214   3rd Qu.:1.500   3rd Qu.:2.4021  
##  Max.   :5.190   Max.   :3.5143   Max.   :2.190   Max.   :3.5021  
##  NA's   :1841    NA's   :1677     NA's   :3150    NA's   :1847    
##      ARCLK             ASELS             ASUZU             AYGAZ        
##  Min.   : 0.0001   Min.   : 0.0001   Min.   : 0.0001   Min.   : 0.0001  
##  1st Qu.:11.7111   1st Qu.: 4.9403   1st Qu.: 5.0748   1st Qu.: 5.9515  
##  Median :15.0100   Median : 9.2757   Median : 5.9496   Median : 7.7238  
##  Mean   :15.3881   Mean   :13.4325   Mean   : 6.4670   Mean   : 8.1019  
##  3rd Qu.:19.0877   3rd Qu.:22.7567   3rd Qu.: 7.1200   3rd Qu.:10.2690  
##  Max.   :26.4278   Max.   :46.7616   Max.   :15.2800   Max.   :13.5935  
##  NA's   :967       NA's   :1209      NA's   :1579      NA's   :1893     
##      BAGFS             BANVT            BRISA             CCOLA        
##  Min.   : 0.0001   Min.   : 0.000   Min.   : 0.0001   Min.   : 0.0001  
##  1st Qu.: 8.2618   1st Qu.: 2.590   1st Qu.: 5.8900   1st Qu.:31.9782  
##  Median :10.6100   Median : 3.710   Median : 6.7300   Median :34.8215  
##  Mean   :10.4071   Mean   : 7.628   Mean   : 6.5449   Mean   :36.8907  
##  3rd Qu.:12.3500   3rd Qu.:11.930   3rd Qu.: 7.3300   3rd Qu.:42.0497  
##  Max.   :38.4352   Max.   :28.680   Max.   :10.3275   Max.   :54.2208  
##  NA's   :1362      NA's   :2061     NA's   :1075      NA's   :1263     
##      CEMAS           ECILC            EREGL             FROTO        
##  Min.   :0.000   Min.   :0.0001   Min.   : 0.0001   Min.   : 0.0001  
##  1st Qu.:0.700   1st Qu.:1.1723   1st Qu.: 2.1812   1st Qu.:21.4938  
##  Median :0.870   Median :1.8214   Median : 3.0360   Median :27.1182  
##  Mean   :1.209   Mean   :2.0759   Mean   : 4.1795   Mean   :32.7637  
##  3rd Qu.:1.500   3rd Qu.:2.7809   3rd Qu.: 6.7587   3rd Qu.:48.5116  
##  Max.   :7.010   Max.   :4.2278   Max.   :10.4710   Max.   :65.4192  
##  NA's   :3618    NA's   :1520     NA's   :839       NA's   :1017     
##      GARAN             GOODY             GUBRF             HALKB        
##  Min.   : 0.0001   Min.   : 0.0001   Min.   : 0.0001   Min.   : 0.0001  
##  1st Qu.: 7.0154   1st Qu.: 2.4277   1st Qu.: 3.2765   1st Qu.: 8.7205  
##  Median : 7.6542   Median : 3.1920   Median : 4.2500   Median :10.6531  
##  Mean   : 7.8997   Mean   : 3.1025   Mean   : 4.3283   Mean   :10.9194  
##  3rd Qu.: 8.6786   3rd Qu.: 3.5966   3rd Qu.: 5.1300   3rd Qu.:13.4909  
##  Max.   :12.1554   Max.   :58.7574   Max.   :13.6191   Max.   :20.2365  
##  NA's   :704       NA's   :1051      NA's   :955       NA's   :941      
##      ICBCT            ISCTR         ISDMR             ISFIN      
##  Min.   : 0.000   Min.   :0.0001   Mode:logical   Min.   :0.000  
##  1st Qu.: 1.560   1st Qu.:4.3200   TRUE:12227     1st Qu.:0.564  
##  Median : 2.030   Median :4.8543   NA's:37785     Median :0.864  
##  Mean   : 2.829   Mean   :5.1266                  Mean   :1.559  
##  3rd Qu.: 4.070   3rd Qu.:5.8203                  3rd Qu.:1.674  
##  Max.   :11.270   Max.   :7.9639                  Max.   :9.830  
##  NA's   :5676     NA's   :791                     NA's   :7135   
##      ISYAT           KAREL           KARSN            KCHOL        
##  Min.   :0.000   Min.   :0.000   Min.   :0.0001   Min.   : 0.0001  
##  1st Qu.:0.441   1st Qu.:1.531   1st Qu.:1.1100   1st Qu.: 9.7368  
##  Median :0.496   Median :1.820   Median :1.2874   Median :12.0449  
##  Mean   :0.537   Mean   :3.178   Mean   :1.3269   Mean   :12.2483  
##  3rd Qu.:0.633   3rd Qu.:5.250   3rd Qu.:1.4700   3rd Qu.:15.1693  
##  Max.   :1.150   Max.   :9.460   Max.   :2.5000   Max.   :19.1500  
##  NA's   :6828    NA's   :3980    NA's   :1485     NA's   :919      
##      KRDMB            KRDMD            MGROS             OTKAR         
##  Min.   :0.0001   Min.   :0.0001   Min.   : 0.0001   Min.   :  0.0001  
##  1st Qu.:1.5612   1st Qu.:1.0845   1st Qu.:16.6600   1st Qu.: 56.7757  
##  Median :2.2007   Median :1.3979   Median :19.1100   Median : 82.8224  
##  Mean   :2.2228   Mean   :1.7684   Mean   :19.5764   Mean   : 81.4195  
##  3rd Qu.:2.7273   3rd Qu.:2.1690   3rd Qu.:22.1000   3rd Qu.:105.4988  
##  Max.   :4.4960   Max.   :4.9510   Max.   :30.2600   Max.   :139.4288  
##  NA's   :2480     NA's   :851      NA's   :1109      NA's   :1227      
##      PARSN            PETKM          PGSUS             PRKME       
##  Min.   : 0.000   Min.   :0.0001   Mode :logical   Min.   :0.0001  
##  1st Qu.: 4.570   1st Qu.:1.2869   FALSE:1         1st Qu.:2.3895  
##  Median : 7.890   Median :2.2845   TRUE :45220     Median :2.7400  
##  Mean   : 8.277   Mean   :2.5392   NA's :4791      Mean   :2.9271  
##  3rd Qu.:10.650   3rd Qu.:3.8828                   3rd Qu.:3.4365  
##  Max.   :29.820   Max.   :5.7697                   Max.   :5.4300  
##  NA's   :4687     NA's   :828                      NA's   :1546    
##      SAHOL              SASA             SISE            SKBNK       
##  Min.   : 0.0001   Min.   :0.0001   Min.   :0.0001   Min.   :0.0001  
##  1st Qu.: 7.9652   1st Qu.:0.3192   1st Qu.:1.9220   1st Qu.:1.2000  
##  Median : 8.6079   Median :0.7335   Median :2.6682   Median :1.5100  
##  Mean   : 8.6159   Mean   :2.2949   Mean   :3.0484   Mean   :1.4737  
##  3rd Qu.: 9.2682   3rd Qu.:4.9473   3rd Qu.:4.1460   3rd Qu.:1.7207  
##  Max.   :11.6826   Max.   :8.4260   Max.   :6.9230   Max.   :2.2516  
##  NA's   :917       NA's   :2379     NA's   :922      NA's   :2742    
##       SODA            TCELL             THYAO             TKFEN        
##  Min.   :0.0001   Min.   : 0.0001   Min.   : 0.0001   Min.   : 0.0001  
##  1st Qu.:1.4758   1st Qu.: 8.5663   1st Qu.: 6.4300   1st Qu.: 4.3190  
##  Median :2.6684   Median : 9.7001   Median : 7.7800   Median : 5.7532  
##  Mean   :3.1896   Mean   : 9.8280   Mean   : 9.2888   Mean   : 9.1918  
##  3rd Qu.:4.2861   3rd Qu.:11.2364   3rd Qu.:12.2700   3rd Qu.:14.2468  
##  Max.   :7.7659   Max.   :15.8125   Max.   :19.9500   Max.   :27.3200  
##  NA's   :1736     NA's   :869       NA's   :730       NA's   :1082     
##      TOASO             TRKCM             TSKB            TTKOM       
##  Min.   : 0.0001   Min.   :0.0001   Min.   :0.0001   Min.   :0.0001  
##  1st Qu.:10.3656   1st Qu.:1.1742   1st Qu.:0.8254   1st Qu.:5.2673  
##  Median :16.5554   Median :1.6270   Median :0.9373   Median :5.7464  
##  Mean   :16.5973   Mean   :2.0278   Mean   :0.9452   Mean   :5.6607  
##  3rd Qu.:20.6513   3rd Qu.:2.9826   3rd Qu.:1.0244   3rd Qu.:6.2600  
##  Max.   :29.9218   Max.   :4.6432   Max.   :1.4208   Max.   :7.3500  
##  NA's   :1066      NA's   :1126     NA's   :1628     NA's   :935     
##      TUKAS           TUPRS               USAK            VAKBN       
##  Min.   :0.650   Min.   :  0.0001   Min.   :0.0001   Min.   :0.0001  
##  1st Qu.:1.060   1st Qu.: 34.5491   1st Qu.:0.9571   1st Qu.:4.0322  
##  Median :1.530   Median : 49.5542   Median :1.0500   Median :4.4742  
##  Mean   :1.738   Mean   : 62.9945   Mean   :1.2205   Mean   :4.7354  
##  3rd Qu.:2.130   3rd Qu.: 93.4287   3rd Qu.:1.3708   3rd Qu.:5.2460  
##  Max.   :5.920   Max.   :139.2937   Max.   :2.7578   Max.   :7.5814  
##  NA's   :4083    NA's   :869        NA's   :2353     NA's   :800     
##      VESTL            YATAS            YKBNK            YUNSA      
##  Min.   : 0.000   Min.   : 0.000   Min.   :0.0001   Min.   :0.000  
##  1st Qu.: 4.020   1st Qu.: 0.389   1st Qu.:2.2682   1st Qu.:3.007  
##  Median : 6.320   Median : 0.966   Median :2.6093   Median :4.108  
##  Mean   : 5.943   Mean   : 2.434   Mean   :2.5663   Mean   :4.080  
##  3rd Qu.: 7.450   3rd Qu.: 4.230   3rd Qu.:2.8740   3rd Qu.:4.721  
##  Max.   :14.540   Max.   :10.675   Max.   :3.9581   Max.   :9.528  
##  NA's   :1231     NA's   :3957     NA's   :787      NA's   :4484   
##      ZOREN       
##  Min.   :0.0001  
##  1st Qu.:1.0338  
##  Median :1.2500  
##  Mean   :1.2481  
##  3rd Qu.:1.4265  
##  Max.   :2.4430  
##  NA's   :1205

First I wanted to see the Five Number Summary Statistics (summary) of each dataset. I realized that there are many missing values (NAs) and I decide to get rid off them

Dataset1 = Dataset[complete.cases(Dataset),] #removing NAs

Then instead of dealing with 61 different stocks, I decide to choose 10 of them. I chose the foloowing 10 stocks because I have an insight about them due to my brother’s trades and advices on Turkish financial market.

AEFES = Dataset1$AEFES
AKBNK = Dataset1$AKBNK
AKSA = Dataset1$AKSA
AKSEN = Dataset1$AKSEN
SASA = Dataset1$SASA
CCOLA = Dataset1$CCOLA
GARAN = Dataset1$GARAN
MGROS = Dataset1$MGROS 
TCELL = Dataset1$TCELL
TUPRS = Dataset1$TUPRS

4.1 Descriptive Analysis

First I will combine them to see the correlation relationships

Table = cbind(AKBNK,AKSA,AKSEN,SASA,CCOLA,GARAN,MGROS,TCELL, TUPRS) # I construct a new table to see the pairs
pairs(Table) # scatter diagrams of each pairs

It seems like there is positive strong correlation between AKBNK and GARAN. Let’s investigate further

plot(AKBNK, GARAN)

round(cor(AKBNK, GARAN),3) # r = 0.907 indicates a strong positive correlation between AKBNK and GARAN.
## [1] 0.907
summary(AKBNK)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   4.607   5.851   6.323   6.433   6.820   9.212
summary(GARAN)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   5.640   7.590   8.220   8.272   8.990  12.098
boxplot(AKBNK) # This function visualize 5-number-summary statistics of AKBNK stock

boxplot(GARAN) # This function visualize 5-number-summary statistics of GARAN stock

To finalize descriptive statistics of each stock we have to define standard deviation, variance, mode, interquartile range, and finally the histogram of each stock.

mode_AKBNK = sort(table(AKBNK), decreasing=T)
mode_AKBNK[1] #mode of AKBNK stock is 6.79
## 6.79 
##   52
sd(AKBNK) #standard deviation of AKBNK
## [1] 0.8210988
var(AKBNK) #variance of AKBNK
## [1] 0.6742033
IQR(AKBNK) #interquartile range of AKBNK
## [1] 0.9691
hist(AKBNK, main="The histogram of stock AKBNK", col="skyblue")

mode_GARAN = sort(table(GARAN), decreasing=T)
mode_GARAN[1] #mode of GARAN stock is 8.95
## 8.95 
##   62
sd(GARAN) #standard deviation of GARAN
## [1] 1.074116
var(GARAN) #variance of GARAN
## [1] 1.153726
IQR(GARAN) #interquartile range of GARAN
## [1] 1.4
hist(GARAN,main="The histogram of stock GARAN", col="skyblue")

2nd finding: It seems like there is positive correlation between AKSA and AKSEN. Let’s investigate further

summary(AKSA)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   5.367   7.941   8.520   8.813   9.685  15.110
summary(AKSEN)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.040   2.518   3.020   3.231   3.990   5.190
boxplot(AKSA) # This function visualize 5-number-summary statistics of AKSA stock

boxplot(AKSEN) # This function visualize 5-number-summary statistics of AKSEN stock

plot(AKSA, AKSEN)

round(cor(AKSA, AKSEN),3) # 0.636 indicates a positive correlation between AKSA and AKSEN.
## [1] 0.636

To finalize descriptive statistics of each stock we have to define standard deviation, variance, mode, interquartile range, and finally the histogram of each stock.

mode_AKSA = sort(table(AKSA), decreasing=T)
mode_AKSA[1] #mode of AKSA stock is 8.0397
## 8.0397 
##     50
sd(AKSA) #standard deviation of AKSA
## [1] 1.575767
var(AKSA) #variance of AKSA
## [1] 2.48304
IQR(AKSA) #interquartile range of AKSA
## [1] 1.743575
hist(AKSA, main="The histogram of stock AKSA", col="skyblue")

mode_AKSEN = sort(table(AKSEN), decreasing=T)
mode_AKSEN[1] #mode of AKSEN stock is 2.35
## 2.35 
##  158
sd(AKSEN) #standard deviation of AKSEN
## [1] 0.7504789
var(AKSEN) #variance of AKSEN
## [1] 0.5632186
IQR(AKSEN) #interquartile range of AKSEN
## [1] 1.4725
hist(AKSEN, main="The histogram of stock AKSEN", col="skyblue")

4.2 Moving Window Correlation

AKBNK_april = AKBNK[11:58]; AKBNK_april
##  [1] 6.4277 6.3155 6.3075 6.3475 6.4677 6.4036 6.3877 6.4117 6.2914 6.3556
## [11] 6.2674 6.2914 6.2995 6.3716 6.3796 6.4117 6.4438 6.5318 6.5078 6.5158
## [21] 6.4838 6.5078 6.5720 6.7643 6.7483 6.7803 6.7883 6.7964 6.9566 6.9807
## [31] 7.0127 6.9646 6.8204 6.8204 6.8926 6.8445 6.8364 6.8204 6.7803 6.6921
## [41] 6.6761 6.8685 6.8926 6.8605 6.8765 6.9086 6.9325 6.8926
AKBNK_may = AKBNK[59:101]
AKBNK_june = AKBNK[102:150]
AKBNK_july = AKBNK[151:182]
AKBNK_august = AKBNK[183:224]
AKBNK_september = AKBNK[225:269]

GARAN_april = GARAN[11:58]; GARAN_april
##  [1] 7.5045 7.3764 7.3764 7.4039 7.6599 7.5776 7.5776 7.5959 7.4314 7.5045
## [11] 7.3764 7.3582 7.3764 7.4862 7.4954 7.5136 7.5684 7.5959 7.5868 7.5410
## [21] 7.4497 7.4679 7.5228 7.6416 7.6142 7.6233 7.6325 7.7787 7.9798 7.9889
## [31] 8.0255 8.0529 7.9707 7.9889 8.0529 7.9066 7.9066 7.7329 7.7378 7.7192
## [41] 7.7378 7.9050 7.9515 7.9050 7.9329 8.0072 8.0444 8.0072
GARAN_may = GARAN[59:101]
GARAN_june = GARAN[102:150]
GARAN_july = GARAN[151:182]
GARAN_august = GARAN[183:224]
GARAN_september = GARAN[225:269]

plot(GARAN_april, AKBNK_april)

cor(GARAN_april, AKBNK_april)
## [1] 0.9288523
plot(GARAN_may, AKBNK_may)

cor(GARAN_may, AKBNK_may)
## [1] 0.819365
plot(GARAN_june, AKBNK_june)

cor(GARAN_june, AKBNK_june)
## [1] 0.7575476
plot(GARAN_july, AKBNK_july)

cor(GARAN_july, AKBNK_july)
## [1] 0.9934856
plot(GARAN_august, AKBNK_august)

cor(GARAN_august, AKBNK_august)
## [1] 0.9493835
plot(GARAN_september, AKBNK_september)

cor(GARAN_september, AKBNK_september)
## [1] 0.925077
AKBNK_2016 = AKBNK[1:376]; AKBNK_2016
##   [1] 6.2904 6.2510 6.2510 6.2904 6.2432 6.2353 6.3475 6.4117 6.4036 6.4117
##  [11] 6.4277 6.3155 6.3075 6.3475 6.4677 6.4036 6.3877 6.4117 6.2914 6.3556
##  [21] 6.2674 6.2914 6.2995 6.3716 6.3796 6.4117 6.4438 6.5318 6.5078 6.5158
##  [31] 6.4838 6.5078 6.5720 6.7643 6.7483 6.7803 6.7883 6.7964 6.9566 6.9807
##  [41] 7.0127 6.9646 6.8204 6.8204 6.8926 6.8445 6.8364 6.8204 6.7803 6.6921
##  [51] 6.6761 6.8685 6.8926 6.8605 6.8765 6.9086 6.9325 6.8926 6.8525 6.7483
##  [61] 6.4677 6.4597 6.4357 6.2434 6.0751 6.1231 6.1391 6.1151 6.2033 6.2273
##  [71] 6.2113 6.2273 6.1391 6.1471 6.1952 6.1873 6.1712 6.1471 6.1712 6.1632
##  [81] 6.2033 6.0110 6.0751 6.0991 6.0590 6.1552 6.1792 6.1873 6.0110 6.1632
##  [91] 6.4518 6.4757 6.3636 6.3556 6.3075 6.3316 6.3716 6.4117 6.4117 6.4838
## [101] 6.3877 6.3475 6.3316 6.3556 6.2514 6.2674 6.4117 6.4117 6.4197 6.4518
## [111] 6.4677 6.5078 6.3395 6.3235 6.3475 6.4518 6.4277 6.3636 6.3475 6.3155
## [121] 6.2834 6.2914 6.2514 6.2594 6.2754 6.2353 6.2594 6.2434 6.3075 6.2995
## [131] 6.2914 6.2674 6.1712 6.1632 6.2273 6.3796 6.4757 6.5720 6.5720 6.6040
## [141] 6.5960 6.5799 6.4036 6.5399 6.5478 6.5559 6.4998 6.5799 6.5799 6.5799
## [151] 6.6761 6.6681 6.7563 6.7242 6.7563 7.0849 7.0768 7.0689 7.0849 7.0768
## [161] 7.1410 7.0207 6.5960 6.5880 6.4597 6.3877 6.3556 6.1792 6.0910 5.9469
## [171] 6.0590 5.9469 5.9628 6.0670 6.1312 6.1312 6.1712 6.0349 6.1792 6.0910
## [181] 6.0910 6.0590 6.2273 6.2594 6.1391 6.1312 6.1312 6.0349 6.0030 6.2193
## [191] 6.1792 6.3316 6.4277 6.4438 6.4917 6.4518 6.5399 6.5960 6.5078 6.5078
## [201] 6.5559 6.5559 6.4036 6.4197 6.5559 6.5158 6.5158 6.5238 6.5639 6.5720
## [211] 6.4998 6.5158 6.5478 6.4357 6.4357 6.2273 6.2353 6.2754 6.4036 6.4036
## [221] 6.3475 6.2754 6.2914 6.2834 6.3235 6.3235 6.3316 6.4277 6.4917 6.5639
## [231] 6.5880 6.5960 6.5880 6.5960 6.5238 6.5720 6.5720 6.6040 6.5639 6.5559
## [241] 6.4518 6.4998 6.4597 6.4357 6.4917 6.6360 6.5880 6.5720 6.5960 6.6281
## [251] 6.7163 6.7563 6.7483 6.7483 6.7403 6.4036 6.3636 6.5158 6.5158 6.5318
## [261] 6.6441 6.6601 6.6441 6.5318 6.5158 6.4597 6.4357 6.4438 6.4838 6.5399
## [271] 6.5399 6.4677 6.4117 6.5238 6.4917 6.4917 6.5478 6.5078 6.4998 6.4917
## [281] 6.5158 6.5318 6.5078 6.3475 6.4036 6.6601 6.6842 6.7563 6.7483 6.7082
## [291] 6.7082 6.7483 6.7643 6.7563 6.7563 6.6601 6.6521 6.6601 6.6761 6.6761
## [301] 6.6601 6.5639 6.5639 6.5720 6.5720 6.6120 6.6360 6.6681 6.5238 6.5318
## [311] 6.4917 6.5158 6.3877 6.2834 6.1712 6.1712 6.2674 6.2754 6.3155 6.2033
## [321] 6.3316 6.4117 6.3716 6.1952 6.3235 6.2273 6.2353 6.2674 6.3235 6.3796
## [331] 6.4036 6.2353 6.0910 6.1552 6.2033 6.1792 6.1312 5.9789 5.9789 5.9469
## [341] 5.9228 6.0910 6.0751 6.1632 6.1231 6.0751 6.0751 6.1151 6.2514 6.2594
## [351] 6.2434 6.3075 6.3155 6.2514 6.3075 6.3716 6.3796 6.3877 6.3075 6.2914
## [361] 6.2434 6.2754 6.2914 6.3155 6.2754 6.2434 6.2353 6.1873 6.2033 6.1471
## [371] 6.2434 6.2434 6.2273 6.2273 6.2674 6.2434
AKBNK_2017 = AKBNK[377:1055]
AKBNK_2018 = AKBNK[1056:5318]
AKBNK_2019 = AKBNK[5319:9228]

GARAN_2016 = GARAN[1:376]; GARAN_2016
##   [1] 7.2669 7.2577 7.2943 7.3126 7.2302 7.2211 7.3126 7.4131 7.4222 7.5136
##  [11] 7.5045 7.3764 7.3764 7.4039 7.6599 7.5776 7.5776 7.5959 7.4314 7.5045
##  [21] 7.3764 7.3582 7.3764 7.4862 7.4954 7.5136 7.5684 7.5959 7.5868 7.5410
##  [31] 7.4497 7.4679 7.5228 7.6416 7.6142 7.6233 7.6325 7.7787 7.9798 7.9889
##  [41] 8.0255 8.0529 7.9707 7.9889 8.0529 7.9066 7.9066 7.7329 7.7378 7.7192
##  [51] 7.7378 7.9050 7.9515 7.9050 7.9329 8.0072 8.0444 8.0072 7.9700 7.9050
##  [61] 7.5521 7.5614 7.5242 7.3663 7.1619 7.0597 7.0318 6.9297 6.9947 7.0133
##  [71] 7.0226 7.0690 7.0133 6.9854 7.0411 6.9854 6.9761 6.9297 6.9575 6.9761
##  [81] 7.0411 6.8182 6.8832 6.9389 6.8646 6.9111 6.9204 6.9389 6.7346 6.8182
##  [91] 7.1619 7.2084 7.0411 7.0318 6.9482 7.0133 7.0040 7.0411 7.0318 7.0783
## [101] 7.0226 6.8925 6.8739 6.8925 6.8089 6.8368 7.0411 7.0411 7.0690 7.1155
## [111] 7.1155 7.1619 7.0226 7.0411 7.0690 7.1805 7.1526 7.0969 7.0690 7.0597
## [121] 6.9947 6.9947 6.9668 6.9389 6.9482 6.9297 6.9297 6.9297 7.0226 6.9761
## [131] 6.9854 6.9204 6.9111 6.8925 6.9668 6.9668 7.0876 7.1991 7.2084 7.2176
## [141] 7.1805 7.2269 6.9482 6.9854 6.9947 7.0133 6.9947 7.1805 7.1712 7.0504
## [151] 7.2641 7.2641 7.3663 7.4220 7.4499 7.6449 7.6542 7.7564 7.7657 7.7471
## [161] 7.8121 7.5985 7.1340 7.1340 7.0226 6.9668 6.9482 6.7717 6.7067 6.5210
## [171] 6.6510 6.5767 6.5674 6.7067 6.7624 6.7717 6.8275 6.6695 6.8089 6.7717
## [181] 6.7717 6.7531 6.8925 6.9668 6.8646 6.8646 6.8553 6.7810 6.7439 6.9854
## [191] 7.0690 7.2827 7.3105 7.3105 7.3384 7.1340 7.3291 7.3477 7.2548 7.2548
## [201] 7.3105 7.3663 7.2269 7.2548 7.3477 7.3105 7.3198 7.3291 7.3291 7.3384
## [211] 7.2548 7.2734 7.3013 7.2269 7.2176 7.0133 7.0411 7.1155 7.2362 7.2269
## [221] 7.1898 7.0411 7.0411 7.0876 7.1155 7.0876 7.0969 7.3570 7.4406 7.5149
## [231] 7.5521 7.5242 7.5242 7.5335 7.5335 7.5707 7.5985 7.6077 7.5892 7.5335
## [241] 7.5056 7.5892 7.5242 7.4963 7.5707 7.7192 7.6635 7.6449 7.6728 7.6635
## [251] 7.7935 7.8957 7.8864 7.8864 7.8028 7.4313 7.3477 7.4778 7.4778 7.5149
## [261] 7.5799 7.5985 7.6263 7.5149 7.4685 7.4034 7.4034 7.3849 7.4592 7.4871
## [271] 7.5149 7.4406 7.4034 7.4871 7.4778 7.4871 7.5521 7.4963 7.4685 7.4499
## [281] 7.4685 7.4963 7.4685 7.3013 7.4034 7.5521 7.5799 7.6635 7.6542 7.6263
## [291] 7.6356 7.6913 7.7564 7.7471 7.7657 7.7285 7.7285 7.7657 7.8214 7.8214
## [301] 7.8121 7.7099 7.7192 7.7006 7.7006 7.7471 7.8214 7.8586 7.6542 7.6728
## [311] 7.5799 7.5799 7.4871 7.3663 7.1155 7.1155 7.2548 7.2176 7.1991 7.0504
## [321] 7.2084 7.3013 7.2269 7.0504 7.1433 7.0597 7.0690 7.0783 7.1619 7.1062
## [331] 7.1155 6.9389 6.7810 6.8089 6.8646 6.8460 6.8275 6.6788 6.6881 6.8182
## [341] 6.8089 6.9761 6.9947 7.0226 6.9761 6.9575 6.9482 6.9482 7.0876 7.0969
## [351] 7.0969 7.0690 7.0597 7.0040 7.0876 7.1712 7.1805 7.1898 7.1433 7.1712
## [361] 7.0876 7.1155 7.1712 7.1991 7.2269 7.1898 7.1898 7.0690 7.0876 7.0133
## [371] 7.1062 7.0969 7.0690 7.0783 7.0783 7.0690
GARAN_2017 = GARAN[377:1055]
GARAN_2018 = GARAN[1056:5318]
GARAN_2019 = GARAN[5319:9228]

plot(GARAN_2016, AKBNK_2016)

cor(GARAN_2016, AKBNK_2016)
## [1] 0.8624163
plot(GARAN_2017, AKBNK_2017)

cor(GARAN_2017, AKBNK_2017)
## [1] 0.9453328
plot(GARAN_2018, AKBNK_2018)

cor(GARAN_2018, AKBNK_2018)
## [1] 0.9566644
plot(GARAN_2019, AKBNK_2019)

cor(GARAN_2019, AKBNK_2019)
## [1] 0.9311119

4.3 Principal Component Analysis (PCA)

numerical_data = Dataset1[2:61]
data_normalized <- scale(numerical_data)
head(data_normalized)
##           AEFES      AKBNK       AKSA      AKSEN     ALARK     ALBRK     ANACM
## [1,] -0.6713347 -0.1741357 -1.0239060 -0.8808708 -2.274540 0.4699192 -3.886826
## [2,] -0.7879552 -0.2221202 -0.9317604 -0.8941956 -2.265639 0.3781936 -3.910856
## [3,] -0.8365774 -0.2221202 -0.9317604 -0.9075205 -2.274540 0.4248166 -3.910856
## [4,] -0.8365774 -0.1741357 -0.9230027 -0.8941956 -2.238715 0.4248166 -3.898841
## [5,] -0.7296710 -0.2316196 -0.9273181 -0.9075205 -2.203113 0.4699192 -3.850553
## [6,] -0.6519066 -0.2412409 -0.9317604 -0.9075205 -2.203113 0.4699192 -3.850553
##            ARCLK     ASELS     ASUZU     AYGAZ    BAGFS     BANVT    BRISA
## [1,] -0.04826430 -3.033768 -1.551689 -1.939165 3.848593 -2.951394 2.039219
## [2,] -0.02479650 -3.040067 -1.577119 -2.002972 3.772594 -2.969511 2.005148
## [3,] -0.05162206 -3.043228 -1.575443 -2.002972 3.752327 -2.975550 2.005148
## [4,] -0.04494304 -3.032700 -1.563595 -1.985643 3.797927 -2.984608 2.520925
## [5,]  0.04232216 -3.040067 -1.509323 -1.974002 3.797927 -3.002725 2.194713
## [6,]  0.05911095 -3.043228 -1.505913 -1.968136 3.797927 -3.005745 2.212836
##         CCOLA     CEMAS     ECILC     EREGL     FROTO      GARAN      GOODY
## [1,] 1.266225 -1.034649 -2.547866 -3.361842 -2.841710 -0.9357146 -0.4832547
## [2,] 1.220707 -1.044689 -2.547866 -3.323912 -2.878351 -0.9442798 -0.4789407
## [3,] 1.207762 -1.034649 -2.559409 -3.319127 -2.892590 -0.9102052 -0.4703129
## [4,] 1.207762 -1.034649 -2.442207 -3.304912 -2.857997 -0.8931680  0.8683042
## [5,] 1.383221 -1.024609 -2.348755 -3.304912 -2.841710 -0.9698822  0.8683042
## [6,] 1.454734 -1.034649 -2.337213 -3.295481 -2.833574 -0.9783543  0.8683042
##         GUBRF    HALKB     ICBCT     ISCTR ISDMR     ISFIN     ISYAT     KAREL
## [1,] 3.407026 1.502065 -1.656840 -1.203885   NaN -1.521447 -1.731656 -2.627192
## [2,] 3.353206 1.450525 -1.663890 -1.213421   NaN -1.517939 -1.689014 -2.627192
## [3,] 3.353206 1.439038 -1.667414 -1.213421   NaN -1.521447 -1.689014 -2.634389
## [4,] 3.407026 1.496412 -1.670939 -1.175383   NaN -1.517939 -1.689014 -2.627192
## [5,] 3.474437 1.439038 -1.656840 -1.175383   NaN -1.517939 -1.689014 -2.619995
## [6,] 3.447527 1.439038 -1.660365 -1.146881   NaN -1.517939 -1.731656 -2.619995
##           KARSN     KCHOL     KRDMB     KRDMD     MGROS     OTKAR     PARSN
## [1,] -0.1806519 -1.417656 -1.152116 -1.498835 0.2732247 0.1726716 -1.514692
## [2,] -0.1394458 -1.345867 -1.221013 -1.539747 0.2342256 0.1270523 -1.505931
## [3,] -0.1806519 -1.373497 -1.221013 -1.549948 0.2316256 0.1270523 -1.503740
## [4,] -0.1394458 -1.340377 -1.221013 -1.549948 0.2472253 0.1371918 -1.501550
## [5,] -0.1394458 -1.378986 -1.255461 -1.549948 0.1614271 0.1118402 -1.453364
## [6,] -0.1806519 -1.362457 -1.255461 -1.560257 0.1614271 0.0966338 -1.455554
##          PETKM PGSUS      PRKME     SAHOL      SASA      SISE    SKBNK
## [1,] -3.260285   NaN -0.7423933 0.5464246 -3.623842 -2.824176 2.134641
## [2,] -3.270608   NaN -0.7590049 0.5372094 -3.627092 -2.841558 2.502474
## [3,] -3.280753   NaN -0.7590049 0.5277871 -3.628752 -2.850484 2.449927
## [4,] -3.250140   NaN -0.6089141 0.5839068 -3.625433 -2.850484 2.502474
## [5,] -3.117897   NaN -0.6923630 0.6678791 -3.623842 -2.789529 2.344832
## [6,] -3.117897   NaN -0.6923630 0.6959390 -3.622183 -2.780603 2.344832
##           SODA     TCELL     THYAO     TKFEN      TOASO     TRKCM      TSKB
## [1,] -2.785086 -1.486513 -2.158276 -2.923705 -0.3407672 -3.423539 0.7260604
## [2,] -2.743362 -1.537597 -2.164857 -2.899013 -0.3300781 -3.433621 0.7260604
## [3,] -2.714242 -1.560285 -2.168147 -2.899013 -0.3300781 -3.443541 0.6889005
## [4,] -2.730837 -1.503631 -2.154986 -2.897346 -0.2819445 -3.423539 0.7260604
## [5,] -2.760036 -1.685346 -2.164857 -2.902292 -0.2819445 -3.404025 0.6517405
## [6,] -2.760036 -1.668295 -2.164857 -2.903940 -0.2659109 -3.404025 0.6139507
##         TTKOM      TUKAS     TUPRS       USAK      VAKBN     VESTL     YATAS
## [1,] 1.778103 -0.7607138 -2.834480 -0.7634023 -0.1576771 -1.431407 -2.677260
## [2,] 1.778103 -0.7525807 -2.836208 -0.7876052 -0.1681164 -1.449260 -2.677260
## [3,] 1.757811 -0.7525807 -2.839660 -0.7876052 -0.1889951 -1.444796 -2.679217
## [4,] 1.778103 -0.7525807 -2.825847 -0.7634023 -0.1473454 -1.435870 -2.677260
## [5,] 1.666392 -0.7607138 -2.832756 -0.7634023 -0.1681164 -1.426944 -2.681107
## [6,] 1.686684 -0.7688469 -2.834480 -0.7876052 -0.1576771 -1.431407 -2.683063
##          YKBNK     YUNSA       ZOREN
## [1,] 1.0379526 -1.763650 -0.09981568
## [2,] 0.9896713 -1.763650 -0.18555073
## [3,] 0.9737434 -1.763650 -0.18555073
## [4,] 1.0217759 -1.756652 -0.18555073
## [5,] 1.0379526 -1.721732 -0.14242021
## [6,] 1.0379526 -1.735729 -0.14242021

First I created the correlation matrix by using thw whole dataset.

corr_matrix <- cor(data_normalized)
ggcorrplot(corr_matrix)

However, we cannot comment much about it. It does not help much, since there are 61 variables. So, I decide to continue principal compenent analysis by using 10 preffered stocks.

Preffered_stock = Table
Preffered_normalized <- scale(Table)
corr_matrix2 <- cor(Preffered_normalized) ;corr_matrix2
##             AKBNK       AKSA       AKSEN        SASA      CCOLA       GARAN
## AKBNK  1.00000000  0.4945576  0.09737377 -0.26715462  0.6847650  0.90683334
## AKSA   0.49455760  1.0000000  0.63575278  0.24921114  0.3338116  0.35995332
## AKSEN  0.09737377  0.6357528  1.00000000  0.27452956  0.2354630 -0.08381838
## SASA  -0.26715462  0.2492111  0.27452956  1.00000000 -0.3838070 -0.07987443
## CCOLA  0.68476501  0.3338116  0.23546301 -0.38380701  1.0000000  0.57486033
## GARAN  0.90683334  0.3599533 -0.08381838 -0.07987443  0.5748603  1.00000000
## MGROS  0.72044582  0.6255036  0.59278858 -0.30141018  0.6744950  0.50030600
## TCELL  0.40664136  0.1212738 -0.17632080  0.38985370  0.1470695  0.64586803
## TUPRS -0.22449139 -0.1178043 -0.28179930  0.66132362 -0.3419093  0.07634485
##              MGROS        TCELL       TUPRS
## AKBNK  0.720445817  0.406641356 -0.22449139
## AKSA   0.625503630  0.121273814 -0.11780427
## AKSEN  0.592788581 -0.176320804 -0.28179930
## SASA  -0.301410184  0.389853704  0.66132362
## CCOLA  0.674494967  0.147069493 -0.34190929
## GARAN  0.500305997  0.645868028  0.07634485
## MGROS  1.000000000  0.001165309 -0.54613207
## TCELL  0.001165309  1.000000000  0.57765782
## TUPRS -0.546132075  0.577657815  1.00000000
ggcorrplot(corr_matrix2)

data.pca <- princomp(corr_matrix2)
summary(data.pca)
## Importance of components:
##                           Comp.1    Comp.2     Comp.3      Comp.4      Comp.5
## Standard deviation     1.0512666 0.6397327 0.23752960 0.097846982 0.081711313
## Proportion of Variance 0.6948427 0.2573108 0.03547287 0.006019434 0.004197833
## Cumulative Proportion  0.6948427 0.9521535 0.98762633 0.993645761 0.997843595
##                             Comp.6       Comp.7       Comp.8       Comp.9
## Standard deviation     0.051265632 0.0239374997 0.0151207619 5.383804e-09
## Proportion of Variance 0.001652393 0.0003602619 0.0001437501 1.822381e-17
## Cumulative Proportion  0.999495988 0.9998562499 1.0000000000 1.000000e+00

We see that highest correlation value appers in between AKBNK and GARAN as we earlier found out.

data.pca$loadings[, 1:2]
##           Comp.1     Comp.2
## AKBNK  0.3594323  0.3291475
## AKSA   0.1980731 -0.2499426
## AKSEN  0.1705985 -0.5475413
## SASA  -0.3926563 -0.1955280
## CCOLA  0.3970042  0.1638051
## GARAN  0.2054261  0.4683821
## MGROS  0.4604257 -0.1034138
## TCELL -0.1618587  0.4374158
## TUPRS -0.4585743  0.2071644
fviz_screeplot(data.pca, addlabels = TRUE)

fviz_pca_var(data.pca, col.var = "black")

fviz_cos2(data.pca, choice = "var", axes = 1:2)

fviz_pca_var(data.pca, col.var = "cos2",
             gradient.cols = c("black", "orange", "green"),
             repel = TRUE)